Optimal Patching in Clustered Malware Epidemics

Abstract

Studies on the propagation of malware in mobile networks have revealed that the spread of malware can be highly inhomogeneous. Platform diversity, contact list utilization by the malware, clustering in the network structure, etc. can also lead to differing spreading rates. In this paper, a general formal framework is proposed for leveraging such heterogeneity to derive optimal patching policies that attain the minimum aggregate cost due to the spread of malware and the surcharge of patching. Using Pontryagin's Maximum Principle for a stratified epidemic model, it is analytically proven that in the mean-field deterministic regime, optimal patch disseminations are simple single-threshold policies. Through numerical simulations, the behavior of optimal patching policies is investigated in sample topologies and their advantages are demonstrated.

Transient Dynamics of Epidemic Spreading and Its Mitigation on Large Networks

“…Corollary 5.2 says that when 0 ≤ x i (0) < 1 for all i, (12) can be simplified to (13), which is essentially from the fact that diag(1 − x(0)) is invertible. Similarly, when x i (0) = 0 or x i (0) = 1 for all i, we have diag(1 − x(0)) (x(0)) = 0 and b(x(0)) = x(0), from which (12) reduces to (14). See the proof of Corollary 5.2 for more details.…”

“…Note that there are other epidemic models. However, the traditional ones, e.g., compartmental model and metapopulation model, neglect the underlying network structure and assume the homogeneous mixing population [13,14], in that every individual has equal chance to contact others in the population or there are multiple homogeneous subgroups, which are clearly far from reality. There have also been other epidemic 'network' models based on the degree-based approximation [29,45,49,50], where the SIS epidemic process is defined on the so-called configuration model, or a random graph with a given degree distribution.…”

The Impact of the Network Topology on the Viral Prevalence: A Node-Based Approach

“…Third, the immunization strategy we adopt also has significant impact on the viral prevalence. To a certain extent, the static immunization problem reduces to that of assigning different curing rates to different nodes so that the best virus containment effect is achieved, given that the sum of curing rates of all nodes is fixed [33, 40], while the dynamic immunization problem can be solved by use of the optimal control theory [41]. Last, but not least, the methodology developed in this work can be applied to the situation of infectious diseases [42–45].…”

Modelling Spreading Process Induced by Agent Mobility in Complex Networks

“…In recent years, epidemic theory has found applications in various different fields, covering virus/disease spreading (both biological and digital ones) (e.g., [1] [5]) and corresponding immunization strategies (e.g., [26] [27] [28] [29]), information dissemination in (online) social networks (e.g., [30]), communication protocol design (e.g., [31] [32] [33]) and cascading failure prediction/protection (e.g., [34]) as well as in more general contexts, analysis on stability of spreading processes over time-varying networks (e.g., [35]) and iden-tification of influential seeds/spreaders in networks (e.g., [36]). …”